"The world is approaching a major turning point in its demographic trajectory and we think that the shift is likely to be sooner and sharper than mainstream projections suggest," Sanyal writes.

In case you've missed it, the global fertility rate has been steadily dropping since 1950.

Sanyal points clients to the Total Fertility Rate (TFR), the average number of live births per women over her lifetime. For most developed countries, the TFR is well below the so-called "replacement rate" of 2.1-2.3. Even in emerging markets like Brazil, the TFR has dropped from 6.2 in the early 1950s to below replacement at 1.8, Sanyal notes.

And in China, the world's most populous country, the TFR is overstated due to a "skewed gender ratio." As Sanyal concludes, "In our view, global fertility will fall to the replacement rate in less than fifteen years."

We feel that the world’s overall fertility rate will fall to replacement rate by 2025. In other words, reproductively speaking, our species will no longer be expanding – a major turning point in history. Of course, overall world population will still expand for a couple more decades due to momentum in the age structure and rising longevity, but this lagged effect will ultimately ease off unless we discover the elixir of immortality. Thus, we forecast that world population will peak around 2055 at 8.7bn and will then decline to 8.0bn by 2100. In other words, our forecasts suggest that world population will peak at least half a century sooner than the UN expects and that by 2100, and that level will be 2.8bn below the UN’s prediction. This is obviously a radically different view of the world.

"We want merely want to alert readers to the strong likelihood that the future trajectory of world population could be an order of magnitude below what conventional projections suggest," Sanyal tells clients.